The actor's girlfriend, 21-year-old Alaina Meyer, is pregnant with the couple's first child.
"We are absolutely over the moon to announce that we will soon be welcoming a little one into this crazy and wonderful world," the parents-to-be tell People.com.
"We ask that you please respect our privacy during this celebratory time for us and our families. There truly is love out there for all. We hope ours is the ember of yours, as we feel yours is the ember of ours."
The couple has been linked since last year (18), with Galecki making the romance Instagram official in September, days after his girlfriend showed off a photo of the 43-year-old's initials tattooed onto her left forearm.
They made their red carpet debut at the 2018 People's Choice Awards in November, and hit headlines again in December, when eagle-eyed fans spotted the pair wearing bands on their left ring fingers in a sweet snap uploaded by Galecki, sparking speculation suggesting they had secretly wed.
However, Meyer dismissed the claims by reposting the image and captioning it, "#notmarried."
Galecki previously dated his TV co-star Kaley Cuoco for two years before breaking things off in 2010. They've remained close friends, and Cuoco has since moved on - she first married tennis player Ryan Sweeting in 2013, and wed second husband Karl Cook last summer.
The baby news emerges as Galecki prepares to bid a final farewell to "The Big Bang Theory", which wrapped filming on its 12th and final season on Tuesday, April 30.
The hit sitcom will sign off as the longest-running multi-camera series in U.S. TV history on 16 May.